The use of the L-curve in the regularization of discrete ill-posed problems
SIAM Journal on Scientific Computing
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Kalman filter approach provides a natural way to include the spatio-temporal prior information in cardiac electrical imaging. This study focuses on the performance of Kalman filter approach with geometric errors present in inverse Electrocardiography (ECG) problem. The geometric errors considered here are the wrong determination of the heart's size and location. In addition to Kalman filtering, we also compare the performances of Tikhonov regularization and Bayesian MAP estimation when geometric errors are present. After presenting the effects of geometric errors on the solutions, a possible model to reduce the effects of the geometric errors in the inverse ECG problem for Bayes-MAP and Kalman solution is studied. To this purpose, a method that is suggested to overcome modeling errors in inverse problem solutions by Heino et. al. is modified and its effectiveness for inverse ECG problem is shown. Here the main idea is to assume geometric errors as additive noise and adding them to the covariance matrices used in the algorithms [1]. To the best of our knowledge, this is the first study in which it has been applied to the inverse problem of ECG.